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42 Gábor Janiga y [mm] 4 2 0 -1 0 1 2 3 x [mm] Fig. 2.13 Zoom on the part of the numerical grid close to the flame front C2H2. The numerical grid is refined adaptively according to a predefined criterion, here the mass fraction of HCO. During the computations, the numerical grid contains up to 8,000 finite-volume cells after reaching the fourth level of grid refinement (see Fig. 2.13). Computations using detailed chemistry with more than 9,000 grid elements are not possible due to memory limitation (2 GB physical memory on a single PC in our system). When using detailed chemistry, a higher resolution or more complex configurations can only be computed on parallel supercomputers [42]. The optimization procedure is carried out on five Pentium-IV PC with 2.6 GHz/2 GB-RAM running under Red Hat 9 Linux. Every computation is performed on a single computer. The computation based on tabulated chemistry used as starting condition for the detailed one takes roughly 90 minutes. Typical computation times for one CFD evaluation with detailed chemistry vary between 9 and 22 hours, depending on the inlet conditions. 2.4.3 Optimization of the Laminar Burner For computing the burner, both the adaptive mesh generation and the flow computations are carried out inside the in-house CFD-software UGC + .To 4
2 A Few Illustrative Examples of CFD-based Optimization 43 illustrate the full computational procedure, the evaluation of an individual set of parameters requires four steps: 1. the computation of the composition of the mixture in the primary and secondary inlet, knowing the specific design variables; 2. the simplified CFD simulation, i.e., the resolution of the governing coupled equations for the flow variables, the energy and the species conservation equations, using first tabulated chemistry (FPI); 3. the high-quality CFD simulation using detailed chemistry and transport models, restarted from the previously obtained FPI solution; 4. the post-processing of the obtained results to extract the values of the objective functions (average mass flow rate of CO along a horizontal cut and maximal variation of the temperature profile along this cut, respectively) for these design variables. For the case considered here, the configuration is two-dimensional and can be optimized on a single PC with a high but acceptable computing time, provided a CFD software as efficient as UGC + is employed. Nevertheless, this will not always be the case. Therefore, a parallel version of this optimization procedure has been developed, as already described for another optimization problem in Sect. 2.3.5. As a whole, 254 configurations have been evaluated during the optimization procedure and 64 feasible cases have been found. The total computational time requested by the optimization using 5 PCs is roughly 3 weeks. The optimization procedure can now be started with the objectives of reducing as much as possible the average mass flow rate of CO and reducing the temperature variations along a horizontal cut through the solution at y =0.025 m, near the outlet. The optimization space is defined, as explained before, by two parameters as shown in Figs. 2.14 and 2.15, where the objective functions are represented as function of the input parameters using a contour plot representation. The darker values correspond to a higher mass flow rate of CO and a higher temperature variation, respectively. The top left corners of these figures contain no results. Since the corresponding input parameters would yield a configuration in contradiction with the concept of a central primary inlet with a surrounding secondary inlet, they are not considered in the procedure. It can be seen that both objectives improve roughly in the same direction in parameter space. Differences are only observed when looking at the details of these evolutions, so that we observe a posteriori that these objectives are in fact not really concurrent, but approach a nearly identical optimum. The differences between both optimal solutions are so small (less than 2 K for the temperature variation) that they probably approach solution accuracy, even using detailed chemistry. All EA parameters are listed in Table 2.4. The two objective values of the feasible cases are shown in Fig. 2.16, in which 20% of the evaluation results are not shown to improve clarity. This
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Optimization and Computational Flui
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Editors: Prof. Dr.-Ing. Dominique T
Page 5 and 6: vi Preface Our first research proje
Page 7 and 8: viii Contents 2.4.1 GoverningEquati
Page 9 and 10: x Contents 6.2.3 Parameterization..
Page 11 and 12: xii Contents 9.4.1 Multi-objectiveO
Page 13 and 14: xiv List of Contributors Gábor JAN
Page 15: Part I Generalities and methods
Page 18 and 19: 4 Dominique Thévenin 12 10 8 6 4 2
Page 20 and 21: 6 Dominique Thévenin Objective 10
Page 22 and 23: 8 Dominique Thévenin Objective 10
Page 24 and 25: 10 Dominique Thévenin Parameter 2
Page 26 and 27: 12 Dominique Thévenin three-dimens
Page 28 and 29: 14 Dominique Thévenin Let us come
Page 30 and 31: 16 Dominique Thévenin References 1
Page 32 and 33: 18 Gábor Janiga 2.1 Introduction D
Page 34 and 35: 20 Gábor Janiga y Tinlet = 293 K 0
Page 36 and 37: 22 Gábor Janiga y [mm] 25 20 15 10
Page 38 and 39: 24 Gábor Janiga Table 2.1 Number o
Page 40 and 41: 26 Gábor Janiga A dominates the in
Page 42 and 43: 28 Gábor Janiga be shown later, th
Page 44 and 45: 30 Gábor Janiga INPUT FILE Gambit
Page 48 and 49: 34 Gábor Janiga ∆T ∆P Position
Page 50 and 51: 36 Gábor Janiga ∆P [mPa] 2.2 2.0
Page 52 and 53: 38 Gábor Janiga Table 2.3 Speed-up
Page 54 and 55: 40 Gábor Janiga For all computatio
Page 58 and 59: 44 Gábor Janiga Air mass flow-rate
Page 60 and 61: 46 Gábor Janiga Temperature variat
Page 64 and 65: 50 Gábor Janiga The modified k-ω
Page 66 and 67: 52 Gábor Janiga Error for Re∗ =
Page 68 and 69: 54 Gábor Janiga Error for Re∗ 20
Page 70 and 71: 56 Gábor Janiga References 1. Ali,
Page 72 and 73: 58 Gábor Janiga 43. Janiga, G., Th
Page 75 and 76: Chapter 3 Mathematical Aspects of C
Page 77 and 78: 3 Mathematical Aspects of CFD-based
Page 93 and 94: Chapter 4 Adjoint Methods for Shape
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4 Adjoint Methods for Shape Optimiz
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Part II Specific Applications of CF
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112 Nicolas R. Gauger Nomenclature
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114 Nicolas R. Gauger Fig. 5.1 Cost
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116 Nicolas R. Gauger and the four
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118 Nicolas R. Gauger CL := 1 � C
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120 Nicolas R. Gauger the cost func
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122 Nicolas R. Gauger Table 5.1 An
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124 Nicolas R. Gauger The main adva
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126 Nicolas R. Gauger Spalart-Allma
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128 Nicolas R. Gauger (a) (b) Fig.
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134 Nicolas R. Gauger Fig. 5.10 Plo
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136 Nicolas R. Gauger drag, lift, s
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138 Nicolas R. Gauger solution of t
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140 Nicolas R. Gauger the presence
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142 Nicolas R. Gauger Fig. 5.16 Con
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144 Nicolas R. Gauger optimization
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Chapter 6 Numerical Optimization fo
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6 Numerical Optimization for Advanc
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192 Laurent Dumas 7.1 Introducing A
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194 Laurent Dumas C Fig. 7.2 Wake f
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196 Laurent Dumas Table 7.1 Example
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198 Laurent Dumas Fig. 7.5 Numerica
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200 Laurent Dumas 7.3.1.1 Genetic A
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202 Laurent Dumas START Random init
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204 Laurent Dumas • if ˜ J(x ng
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206 Laurent Dumas Table 7.3 Compari
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208 Laurent Dumas Fig. 7.9 General
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210 Laurent Dumas Table 7.4 Four ex
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212 Laurent Dumas Fig. 7.13 Blades
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214 Laurent Dumas Table 7.5 Converg
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Chapter 8 Multi-objective Optimizat
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8 Multi-objective Optimization in C
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8 Multi-objective Optimizatio Fig.
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Chapter 9 CFD-based Optimization fo
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9 CFD-based optimization for paperm
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292 Index heat exchanger, 222, 224,
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